TOKYO/NEW YORK, Oct 11 (Reuters) - Japanese mobile carrier Softbank Corp may buy a majority stake in Sprint Nextel Corp to establish a foothold in the U.S. wireless market, in what could be the largest Japanese acquisition ever in America.

But Softbank's ambitions may not stop with Sprint; Nikkei reported that the Japanese company was aiming to use Sprint as a vehicle to make a run at smaller Sprint peer MetroPCS , a two-step transaction that would potentially cost more than 2 trillion yen ($25.55 billion).

That would make for the biggest overseas acquisition by a Japanese company ever, and vault Softbank into the top echelons of wireless carriers worldwide.

In response to reports of a pending deal, Sprint said on Thursday that it was in talks with Softbank on a "potential substantial investment" that could involve a change in control of the U.S. company. It said there was no assurance of a sale.

Softbank is eyeing a controlling stake in Sprint worth more than 1 trillion yen ($12.8 billion), and is in talks with several banks to borrow money to finance a bid, according to a source with direct knowledge of the matter.

A second source familiar with the situation, who would not speak on the matter publicly, said Softbank was after a roughly 70 percent stake in Sprint, which it would achieve by buying some shares directly from Sprint and tendering for the rest.

Sprint shares rose as much as 19 percent on Thursday to levels not seen since the summer of 2011, on the heaviest trading volume in the stock's history. Shares of wireless carrier Clearwire Corp , which could play a key role in any deal, soared 55 percent.

Sprint owns almost half of Clearwire, and a major Sprint investor said any Softbank investment should be used to buy out the rest of Clearwire, which would add attractive high-speed data assets.

"I just don't think there's any deal unless it involves Clearwire. I don't think you'd see one without the other," said Daniel Martino, a fund manager at T. Rowe Price, which owned 47.2 million Sprint shares as of the end of June.

Sprint, whose market capitalization was $15.12 billion at Wednesday's market close, is the third-largest U.S. carrier, with more than 56 million users at the end of June. It is in the middle of a costly network upgrade that has led it to consider a range of partnerships.

One analyst said Sprint might be Softbank's only option if it is eyeing the American market.

"In terms of (Sprint) standalone, we believe the asset represents the only way for a potential new entrant to get a national presence immediately in the U.S.," Wells Fargo analyst Jennifer Fritzsche wrote in a note to clients.

The Softbank news comes just days after a source told Reuters that Sprint has been considering bidding for MetroPCS, which agreed this month to merge with Deutsche Telekom AG's

T-Mobile USA.

MetroPCS shares rose 1 percent in afternoon trading after initially falling sharply. T. Rowe Price's Martino said that if Softbank and Sprint owned Clearwire, they would not need MetroPCS, a company that has been in Sprint's sights for some time.

The atmosphere was calm at Sprint headquarters in Overland Park, Kansas on Thursday.

"This will be interesting to see if it happens; if it has legs," said one longtime Sprint manager who did not want to be named. "There are always a bunch of rumours. Something like this is always a possibility when your stock price is so low."

WEALTHY FOUNDER

A third source familiar with the situation, who declined to speak publicly about the matter, said Softbank has been exploring ways to get into the U.S. market since this summer, as it sees opportunities for growth here that would help offset a stagnating market in Japan.

Founded and led by Masayoshi Son - Japan's second-richest man, according to Forbes - Softbank has grown from a packaged software distributor 30 years ago into a broad telecommunications group worth more than $40 billion.

But it faces tougher competition at home against the likes of KDDI Corp and NTT Docomo .

As it chases market share, Softbank said this month it would buy smaller mobile service operator eAccess Ltd in a $1.84 billion deal. It said the buy would give it a total of 39 million users, just ahead of KDDI's 36 million.

Japanese media said buying Sprint - which competes in the United States against Verizon Wireless and AT&T Inc - would also make it cheaper for Softbank to procure smartphones and other mobile devices.

Wells Fargo's Fritzsche said regulators would likely look favorably on a deal that would bring an outside international player to the United States.

Japanese companies made a record 642 cross-border deals last year, according to Thomson Reuters data. Buoyed by a stronger yen , the value of all overseas deals rose to $69.5 billion, up 81 percent from 2010, also a record.

(Additional reporting by Mari Saito and James Topham in Japan, Sruthi Ramakrishnan in Bangalore, Martinne Geller in New York and Carey Gillam in Overland Park, Kansas; Writing by Ian Geoghegan and Ben Berkowitz; Editing by Bernadette Baum, Andre Grenon and John Wallace)